Analysing Non-Markovian Open Quantum Systems to Understand the Role of the External Environment in Cryptochrome-Based Magnetoreception

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Magnetoreception, the ability of some animals to sense the geomagnetic field, has been a topic of considerable intrigue within the scientific community. Four decades of extensive research have demonstrate unequivocally that the extraordinary ability of migratory birds to navigate is supported by a visual 'magnetic compass'. It is now widely accepted that cryptochromes, a type of flavoprotein within the retinae of migratory birds, are responsible for facilitating this 'sixth sense'. Within cryptochromes, a radical pair is thought to be generated by photoactivation, the quantum coherent spin dynamics of which render the radical pair's subsequent recombination sensitive to the inclination of the Earth's magnetic field.The majority of current models of the avian magnetic compass treat the spin dynamics of the cryptochrome in isolation. However, recent theoretical investigations and experimental studies of the protein's magnetosensitivity in vitro show that the response of an isolated cryptochrome to the geomagnetic fields is far too small to feasibly support navigation. We hypothesize that this 'interaction strength gap' could be understood, and resolved, in terms of interactions of the cryptochrome with its environment, i.e. its open-system nature. Conventionally, one might predict that the noisy biological environment would solely lead to coherence loss in the cryptochrome, thus destroy its sensitivity to the external field. However, our preliminary studies suggest that, counterintuitively, it seems as though the environment itself can reinforce the delicate spin coherences. Specifically, the system-bath interaction can be a source of non-Markovian behaviour, which, under certain conditions, can act as driver of the spin dynamics and enhance the coherence and sensitivity of the system. This is contrary to what is observed in most instances quantum-technological applications for which interactions with an external environment lead to coherence loss and suppression of quantum effects.This project aims to theoretically study the spin dynamics of radical systems subject to non-Markovian noise and driving as a result of their embedding in a biological environment. To this end, we will develop the tools to treat the open-system spin dynamics of realistically complex radical pair systems under conditions of non-Markovian coupling and driving. We will then apply these approaches to radical pair processes in cryptochrome and, in addition, biological radical processes outside of the cryptochrome realm, such as lipid peroxidation. Initial approaches will be based on the framework of the hierarchical equations of motion (HEOM), developed by Tanimura and Kubo, while large, more realistic models will later be realized based on wave function-based extensions to HEOM. Non-Markovian effects have not been previously studied in radical spin dynamics, but preliminary analysis suggests that they hold the key to deciphering magnetoreception. This project will provide the corresponding answer, with far-reaching applications, e.g. for the development biomimetic quantum technology, and implications as to our understanding of quantum effects underpinning biological function.